On extending some primal-dual interior-point algorithms from linear programming to semidefinite programming

SIAM Journal on Optimization

Volumn 8, Issue 2, 1998, Pages 365-386

  Zhang, Yin ^a  

^a RICE UNIVERSITY   (United States)

Author keywords

Primal dual interior point methods; Semidefinite programming

Indexed keywords

EID: 0032081158     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623495296115     Document Type: Article

References (25)

1. F. ALIZADEH, Interior point methods in semidefinite programming with applications to combinatorial optimization, SIAM J. Optim., 5 (1995), pp. 13-51.
2. F. ALIZADEH, J. A. HAEBERLY, AND M. OVERTON, Primal-Dual Interior-Point Methods for Semidefinite Programming: Convergence rates, stability and numerical results, Tech. report 721, Courant Institute of Mathematical Sciences, New York University New York 1996.
3. F. ALIZADEH, J. A. HAEBERLY, AND M. OVERTON, Complementarity and nondegeneracy in semidefinite programming, Math. Programming, 77 (1997), pp. 111-128.
4. S. BOYD, L. GHOUI, E. FERON, AND V. BALAKRISHNAN, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA, 1994.
5. C. HELMBERG, F. RENDL, R. J. VANDERBEI, AND H. WOLKOWICZ, An interior-point method for semidefinite programming, SIAM J. Optim., 6 (1996), pp. 342-361.
6. R. A. HORN AND C. R. JOHNSON, Topics in Matrix Analysis, Cambridge University Press, London, 1991.
7. F. JARRE, An interior-point method for minimizing the maximum eigenvalue of a linear combination of matrices, SIAM J. Control Optim., 31 (1993), pp. 1360-1377.
8. M. KOJIMA, private communication, Tokyo Institute of Technology, Japan, 1995.
9. M. KOJIMA, N. MEGIDDO, AND S. MIZUNO, A primal-dual infeasible-interior-point algorithm for linear programming, Math. Programming, 61 (1993), pp. 263-280.
10. M. KOJIMA, S. MIZUNO, AND A. YOSHISE, A primal-dual interior point method for linear programming, in Progress in mathematical programming, interior-point and related methods, Nimrod Megiddo, ed., Springer-Verlag, New York, 1989, pp. 29-47.
11. M. KOJIMA, S. SHINDOH, AND S. HARA, Interior-point methods for the monotone linear complementarity problem in symmetric matrices, SIAM J. Optim., 7 (1997), pp. 86-125.
12. M. KOJIMA, S. SHINDOH, AND S. HARA, Reduction of monotone linear complementarity problems over cones to linear programs over cones, Acta Math. Vietnam, 22 (1997), pp. 147-157.
13. M. KOJIMA, M. SHIDA, AND S. SHINDOH, Local convergence of predictor-corrector infeasible-interior-point algorithms for SDPs and SDLCPs, Math. Programming, 80 (1998), pp. 129-161.
14. S. MIZUNO, M. J. TODD, AND Y. YE, On adaptive step primal-dual interior-point algorithms for linear programming, Math. Oper. Res., 18 (1993), pp. 964-981.
15. R. C. MONTEIRO, Primal-dual path following algorithms for semidefinite programming, SIAM J. Optim., 7 (1997), pp. 663-678.
16. Y. E. NESTEROV AND A. S. NEMIROVSKII, Interior Point Methods in Convex Programming-Theory and Applications, SIAM, Philadelphia, PA, 1994.
17. Y. E. NESTEROV AND M. TODD, Primal-dual interior-point methods for self-scaled cones, SIAM J. Optim., 8 (1998), pp. 324-364.
18. M. L. OVERTON, On minimizing the maximum eigenvalue of a symmetric matrix, SIAM J. Matrix Anal. Appl., 9 (1988), pp. 256-268.
19. M. L. OVERTON, Large-scale optimization of eigenvalues, SIAM J. Optim., 2 (1992), pp. 88-120.
20. F. A. POTRA AND RONGQIN SHENG, A superlinearly convergent primal-dual infeasible-interior-point algorithm for semidefinite programming, SIAM J. Optim., to appear.
21. M. RAMANA, An exact duality theory for semidefinite programming and its complexity implications, Math. Programming, 77 (1997), pp. 129-162.
22. F. RENDL, R. J. VANDERBEI, AND H. WOLKOWICZ, Max-Min Eigenvalue Problems, primal-dual interior point algorithms, and trust subproblems, Optim. Methods Softw., 5 (1995), pp. 1-16.
23. L. VANDENBERGHE AND S. BOYD, Semidefinite programming, SIAM Rev., 38 (1996), pp. 49-95.
24. L. VANDENBERGHE AND S. BOYD, A primal-dual potential reduction method for problems involving matrix inequalities, Math. Programming, Series B, 69 (1995), pp. 205-236.
25. YIN ZHANG, On the convergence of a class of infeasible interior-point algorithms for the horizontal linear complementarity problem, SIAM J. Optim., 4 (1994), pp. 208-227.